1. Field of Invention
The present invention relates to a method of and system for aggregating data elements in a multi-dimensional database (MDDB) supported upon a computing platform and also to provide an improved method of and system for managing data elements within an MDDB during on-line analytical processing (OLAP) operations and as an integral part of a database management system.
2. Brief Description of the State of the Art
The ability to act quickly and decisively in today's increasingly competitive marketplace is critical to the success of organizations. The volume of information that is available to corporations is rapidly increasing and frequently overwhelming. Those organizations that will effectively and efficiently manage these tremendous volumes of data, and use the information to make business decisions, will realize a significant competitive advantage in the marketplace.
Data warehousing, the creation of an enterprise-wide data store, is the first step towards managing these volumes of data. The Data Warehouse is becoming an integral part of many information delivery systems because it provides a single, central location where a reconciled version of data extracted from a wide variety of operational systems is stored. Over the last few years, improvements in price, performance, scalability, and robustness of open computing systems have made data warehousing a central component of Information Technology CIT strategies. Details on methods of data integration and constructing data warehouses can be found in the white paper entitled “Data Integration: The Warehouse Foundation” by Louis Rolleigh and Joe Thomas.
Building a Data Warehouse has its own special challenges (e.g. using common data model, common business dictionary, etc.) and is a complex endeavor. However, just having a Data Warehouse does not provide organizations with the often-heralded business benefits of data warehousing. To complete the supply chain from transactional systems to decision maker, organizations need to deliver systems that allow knowledge workers to make strategic and tactical decisions based on the information stored in these warehouses. These decision support systems are referred to as On-Line Analytical Processing (OLAP) systems. OLAP systems allow knowledge workers to intuitively, quickly, and flexibly manipulate operational data using familiar business terms, in order to provide analytical insight into a particular problem or line of inquiry. For example, by using an OLAP system, decision makers can “slice and dice” information along a customer (or business) dimension, and view business metrics by product and through time. Reports can be defined from multiple perspectives that provide a high-level or detailed view of the performance of any aspect of the business. Decision makers can navigate throughout their database by drilling down on a report to view elements at finer levels of detail, or by pivoting to view reports from different perspectives. To enable such full-functioned business analyses, OLAP systems need to (1) support sophisticated analyses, (2) scale to large numbers of dimensions, and (3) support analyses against large atomic data sets. These three key requirements are discussed further below.
Decision makers use key performance metrics to evaluate the operations within their domain, and OLAP systems need to be capable of delivering these metrics in a user-customizable format. These metrics may be obtained from the transactional databases pre-calculated and stored in the database, or generated on demand during the query process. Commonly used metrics include:                (1) Multidimensional Ratios (e.g. Percent to Total)—“Show me the contribution to weekly sales and category profit made by all items sold in the Northwest stores between July 1 and July 14.”        (2) Comparisons (e.g. Actual vs. Plan, This Period vs. Last Period)—“Show me the sales to plan percentage variation for this year and compare it to that of the previous year to identify planning discrepancies.”        (3) Ranking and Statistical Profiles (e.g. Top N/Bottom N, 70/30, Quartiles)—“Show me sales, profit and average call volume per day for my 20 most profitable salespeople, who are in the top 30% of the worldwide sales.”        (4) Custom Consolidations—“Show me an abbreviated income statement by quarter for the last two quarters for my Western Region operations.”        
Knowledge workers analyze data from a number of different business perspectives or dimensions. As used hereinafter, a dimension is any element or hierarchical combination of elements in a data model that can be displayed orthogonally with respect to other combinations of elements in the data model. For example, if a report lists sales by week, promotion, store, and department, then the report would be a slice of data taken from a four-dimensional data model.
Target marketing and market segmentation applications involve extracting highly qualified result sets from large volumes of data. For example, a direct marketing organization might want to generate a targeted mailing list based on dozens of characteristics, including purchase frequency, size of the last purchase, past buying trends, customer location, age of customer, and gender of customer. These applications rapidly increase the dimensionality requirements for analysis.
The number of dimensions in OLAP systems range from a few orthogonal dimensions to hundreds of orthogonal dimensions. Orthogonal dimensions in an exemplary OLAP application might include Geography, Time, and Products.
Atomic data refers to the lowest level of data granularity required for effective decision making. In the case of a retail merchandising manager, “atomic data” may refer to information by store, by day, and by item. For a banker, atomic data may be information by account, by transaction, and by branch. Most organizations implementing OLAP systems find themselves needing systems that can scale to tens, hundreds, and even thousands of gigabytes of atomic information.
As OLAP systems become more pervasive and are used by the majority of the enterprise, more data over longer time frames will be included in the data store (i.e. data warehouse), and the size of the database will increase by at least an order of magnitude. Thus, OLAP systems need to be able to scale from present to near-future volumes of data.
In general, OLAP systems need to (1) support the complex analysis requirements of decision-makers, (2) analyze the data from a number of different perspectives (i.e. business dimensions), and (3) support complex analyses against large input (atomic-level) data sets from a Data Warehouse maintained by the organization using a relational database management system (RDBMS).
Vendors of OLAP systems classify OLAP Systems as either Relational OLAP (ROLAP) or Multidimensional OLAP (MOLAP) based on the underlying architecture thereof. Thus, there are two basic architectures for On-Line Analytical Processing systems: the ROLAP Architecture, and the MOLAP architecture.
The Relational OLAP (ROLAP) system accesses data stored in a Data Warehouse to provide OLAP analyses. The premise of ROLAP is that OLAP capabilities are best provided directly against the relational database, i.e. the Data Warehouse.
The ROLAP architecture was invented to enable direct access of data from Data Warehouses, and therefore support optimization techniques to meet batch window requirements and to provide fast response times. Typically, these optimization techniques include application-level table partitioning, pre-aggregate inferencing, denormalization support, and the joining of multiple fact tables.
A typical prior art ROLAP system has a three-tier or layer client/server architecture. The “database layer” utilizes relational databases for data storage, access, and retrieval processes. The “application logic layer” is the ROLAP engine which executes the multidimensional reports from multiple users. The ROLAP engine integrates with a variety of “presentation layers,” through which users perform OLAP analyses.
After the data model for the data warehouse is defined, data from on-line transaction-processing (OLTP) systems is loaded into the relational database management system (RDBMS). If required by the data model, database routines are run to pre-aggregate the data within the RDBMS. Indices are then created to optimize query access times. End users submit multidimensional analyses to the ROLAP engine, which then dynamically transforms the requests into SQL execution plans. The SQL execution plans are submitted to the relational database for processing, the relational query results are cross-tabulated, and a multidimensional result data set is returned to the end user. ROLAP is a fully dynamic architecture capable of utilizing pre-calculated results when they are available, or dynamically generating results from atomic information when necessary.
Multidimensional OLAP (MOLAP) systems utilize a proprietary multidimensional database (MDDB) to provide OLAP analyses. The MDDB is logically organized as a multidimensional array (typically referred to as a multidimensional cube or hypercube or cube) whose rows/columns each represent a different dimension (i.e., relation). A data value is associated with each combination of dimensions (typically referred to as a “coordinate”). The main premise of this architecture is that data must be stored multidimensionally to be accessed and viewed multidimensionally.
As shown in FIG. 1B, prior art MOLAP systems have an Aggregation, Access and Retrieval module which is responsible for all data storage, access, and retrieval processes, including data aggregration (i.e. preaggregation) in the MDDB. As shown in FIG. 1B, the base data loader is fed with base data, in the most detailed level, from the Data Warehouse, into the Multi-Dimensional Data Base (MDDB). On top of the base data, layers of aggregated data are built-up by the Aggregation program, which is part of the Aggregation, Access and Retrieval module. As indicated in this figure, the application logic module is responsible for the execution of all OLAP requests/queries (e.g. ratios, ranks, forecasts, exception scanning, and slicing and dicing) of data within the MDDB. The presentation module integrates with the application logic module and provides an interface, through which the end users view and request OLAP analyses on their client machines which may be web-enabled through the infrastructure of the Internet. The client/server architecture of a MOLAP system allows multiple users to access the same multidimensional database (MDDB).
Information (i.e. basic data) from a variety of operational systems within an enterprise, comprising the Data Warehouse, is loaded into a prior art multidimensional database (MDDB) through a series of batch routines. The Express™ server by the Oracle Corporation is exemplary of a popular server which can be used to carry out the data loading process in prior art MOLAP systems. As shown in FIG. 2B, an exemplary 3-D MDDB is schematically depicted, showing geography, time and products as the “dimensions” of the database. The multidimensional data of the MDDB is logically organized in an array structure, as shown in FIG. 2C. Physically, the Express™ server stores data in pages (or records) of an information file. Pages contain 512, or 2048, or 4096 bytes of data, depending on the platform and the release of the Express™ server. In order to look up the physical record address from the database file recorded on a disk or other mass storage device, the Express™ server generates a data structure referred to as a “Page Allocation Table (PAT)”. As shown in FIG. 2D, the PAT tells the Express™ server the physical record number that contains the page of data. Typically, the PAT is organized in pages. The simplest way to access a data element in the MDDB is by calculating the “offset” using the additions and multiplications expressed by a simple formula:Offset=Months+Product*(# of_Months)+City*(# of_Months*# of_Products)
During an OLAP session, the response time of a multidimensional query on a prior art MDDB depends on how many cells in the MDDB have to be added “on the fly”. As the number of dimensions in the MDDB increases linearly, the number of the cells in the MDDB increases exponentially. However, it is known that the majority of multidimensional queries deal with summarized high level data. Thus, as shown in FIGS. 3A and 3B, once the atomic data (i.e. “basic data”) has been loaded into the MDDB, the general approach is to perform a series of calculations in batch in order to aggregate (i.e. pre-aggregate) the data elements along the orthogonal dimensions of the MDDB and to fill the array structures thereof. For example, revenue figures for all retail stores in a particular state (i.e. New York) would be added together to fill the state level cells in the MDDB. After the array structure in the database has been filled, integer-based indices are created and hashing algorithms are used to improve query access times. Pre-aggregation of dimension D0 is always performed along the cross-section of the MDDB along the D0 dimension.
As shown in FIGS. 3C1 and 3C2, the raw data loaded into the MDDB is primarily organized at its lowest dimensional hierarchy, and the results of the pre-aggregations are stored in the neighboring parts of the MDDB.
As shown in FIG. 3C2, along the TIME dimension, weeks are the aggregation results of days, months are the aggregation results of weeks, and quarters are the aggregation results of months. While not shown in the figures, along the GEOGRAPHY dimension, states are the aggregation results of cities, countries are the aggregation results of states, and continents are the aggregation results of countries. By pre-aggregating (i.e. consolidating or compiling) all logical subtotals and totals along all dimensions of the MDDB, it is possible to carry out real-time MOLAP operations using a multidimensional database (MDDB) containing both basic (i.e. atomic) and pre-aggregated data. Once this compilation process has been completed, the MDDB is ready for use. Users request OLAP reports by submitting queries through the OLAP Application interface (e.g. using web-enabled client machines), and the application logic layer responds to the submitted queries by retrieving the stored data from the MDDB for display on the client machine.
Typically, in MDDB systems, the aggregated data is very sparse, tending to explode as the number of dimension grows and dramatically slowing down the retrieval process (as described in the report entitled “Database Explosion: The OLAP Report”, incorporated herein by reference). Quick and on line retrieval of queried data is critical in delivering an on-line response for OLAP queries. Therefore, the data structure of the MDDB, and methods of its storing, indexing and handling are dictated mainly by the need for fast retrieval of massive and sparse data.
Different solutions for this problem are disclosed in the following U.S. patents, each of which is incorporated herein by reference in its entirety:                U.S. Pat. No. 5,822,751 “Efficient Multidimensional Data Aggregation Operator Implementation”        U.S. Pat. No. 5,805,885 “Method And System For Aggregation Objects”        U.S. Pat. No. 5,781,896 “Method And System For Efficiently Performing Database Table Aggregation Using An Aggregation Index”        U.S. Pat. No. 5,745,764 “Method And System For Aggregation Objects”        
In all the prior art of OLAP servers, the process of storing, indexing and handling MDDB utilize complex data structures to largely improve the retrieval speed, as part of the querying process, at the cost of slowing down the storing and aggregation. The query-bounded structure, that must support fast retrieval of queries in a restricting environment of high sparcity and multi-hierarchies, is not the optimal one for fast aggregation.
In addition to the aggregation process, the Aggregation, Access and Retrieval module is responsible for all data storage, retrieval and access processes. The Logic module is responsible for the execution of OLAP queries. The Presentation module intermediates between the user and the Logic module and provides an interface through which the end users view and request OLAP analyses. The client/server architecture allows multiple users to simultaneously access the multidimensional database.
In summary, general system requirements of OLAP systems include: (1) supporting sophisticated analysis, (2) scaling to a large number of dimensions, and (3) supporting analysis against large atomic data sets.
MOLAP system architecture is capable of providing analytically sophisticated reports and analysis functionality. However, requirements (2) and (3) fundamentally limit MOLAP's capability, because to be effective and to meet end-user requirements, MOLAP databases need a high degree of aggregation.
By contrast, the ROLAP system architecture allows the construction of systems requiring a low degree of aggregation, but such systems are significantly slower than systems based on MOLAP system architecture principles. The resulting long aggregation times of ROLAP systems impose severe limitations on its volumes and dimensional capabilities.
The graphs plotted in FIG. 5 clearly indicate the computational demands that are created when searching an MDDB during an OLAP session, where answers to queries are presented to the MOLAP system, and answers thereto are solicited often under real-time constraints. However, prior art MOLAP systems have limited capabilities to dynamically create data aggregations or to calculate business metrics that have not been precalculated and stored in the MDDB.
The large volumes of data and the high dimensionality of certain market segmentation applications are orders of magnitude beyond the limits of current multidimensional databases.
ROLAP is capable of higher data volumes. However, the ROLAP architecture, despite its high volume and dimensionality superiority, suffers from several significant drawbacks as compared to MOLAP:                Full aggregation of large data volumes are very time consuming, otherwise, partial aggregation severely degrades the query response.        It has a slower query response        It requires developers and end users to know SQL        SQL is less capable of the sophisticated analytical functionality necessary for OLAP        ROLAP provides limited application functionality        
Thus, improved techniques for data aggregation within MOLAP systems would appear to allow the number of dimensions of and the size of atomic (i.e. basic) data sets in the MDDB to be significantly increased, and thus increase the usage of the MOLAP system architecture.
Also, improved techniques for data aggregation within ROLAP systems would appear to allow for maximized query performance on large data volumes, and to reduce the time of partial aggregations that degrades query response, and thus, generally benefit ROLAP system architectures.
Thus, there is a great need in the art for an improved way of and means for aggregating data elements within a multi-dimensional database (MDDB), while avoiding the shortcomings and drawbacks of prior art systems and methodologies.
Modern operational and informational database systems, as described above, typically use a database management system (DBMS) (such as an RDBMS system, object database system, or object/relational database system) as a repository for storing data and querying the data. FIG. 14 illustrates a data warehouse-OLAP domain that utilizes the prior art approaches described above. The data warehouse is an enterprise-wide data store. It is becoming an integral part of many information delivery systems because it provides a single, central location wherein a reconciled version of data extracted from a wide variety of operational systems is stored. Details on methods of data integration and constructing data warehouses can be found in the white paper entitled “Data Integration: The Warehouse Foundation” by Louis Rolleigh and Joe Thomas.
Building a Data Warehouse has its own special challenges (e.g. using common data model, common business dictionary, etc.) and is a complex endeavor. However, just having a Data Warehouse does not provide organizations with the often-heralded business benefits of data warehousing. To complete the supply chain from transactional systems to decision maker, organizations need to deliver systems that allow knowledge workers to make strategic and tactical decisions based on the information stored in these warehouses. These decision support systems are referred to as On-Line Analytical Processing (OLAP) systems. Such OLAP systems are commonly classified as Relational OLAP systems or Multi-Dimensional OLAP systems as described above.
The Relational OLAP (ROLAP) system accesses data stored in a relational database (which is part of the Data Warehouse) to provide OLAP analyses. The premise of ROLAP is that OLAP capabilities are best provided directly against the relational database. The ROLAP architecture was invented to enable direct access of data from Data Warehouses, and therefore support optimization techniques to meet batch window requirements and to provide fast response times. Typically, these optimization techniques include application-level table partitioning, pre-aggregate inferencing, denormalization support, and the joining of multiple fact tables.
As described above, a typical ROLAP system has a three-tier or layer client/server architecture. The “database layer” utilizes relational databases for data storage, access, and retrieval processes. The “application logic layer” is the ROLAP engine which executes the multidimensional reports from multiple users. The ROLAP engine integrates with a variety of “presentation layers,” through which users perform OLAP analyses. After the data model for the data warehouse is defined, data from on-line transaction-processing (OLTP) systems is loaded into the relational database management system (RDBMS). If required by the data model, database routines are run to pre-aggregate the data within the RDBMS. Indices are then created to optimize query access times. End users submit multidimensional analyses to the ROLAP engine, which then dynamically transforms the requests into SQL execution plans. The SQL execution plans are submitted to the relational database for processing, the relational query results are cross-tabulated, and a multidimensional result data set is returned to the end user. ROLAP is a fully dynamic architecture capable of utilizing pre-calculated results when they are available, or dynamically generating results from the raw information when necessary.
The Multidimensional OLAP (MOLAP) systems utilize a proprietary multidimensional database (MDDB) (or “cube”) to provide OLAP analyses. The main premise of this architecture is that data must be stored multidimensionally to be accessed and viewed multidimensionally. Such MOLAP systems provide an interface that enables users to query the MDDB data structure such that users can “slice and dice” the aggregated data. As shown in FIG. 15, such MOLAP systems have an aggregation engine which is responsible for all data storage, access, and retrieval processes, including data aggregation (i.e. pre-aggregation) in the MDDB, and an analytical processing and GUI module responsible for interfacing with a user to provide analytical analysis, query input, and reporting of query results to the user. In a relational database, data is stored in tables. In contrast, the MDDB is a non-relational data structure—it uses other data structures, either instead of or in addition to tables—to store data.
There are other application domains where there is a great need for improved methods of and apparatus for carrying out data aggregation operations. For example, modern operational and informational databases represent such domains. As described above, modern operational and informational databases typically utilize a relational database system (RDBMS) as a repository for storing data and querying data. FIG. 16A illustrates an exemplary table in an RDBMS; and FIGS. 16B and 16C illustrate operators (queries) on the table of FIG. 16A, and the result of such queries, respectively. The operators illustrated in FIGS. 16B and 16C are expressed as Structured Query Language (SQL) statements as is conventional in the art.
The choice of using an RDBMS as the data repository in information database systems naturally stems from the realities of SQL standardization, the wealth of RDBMS-related tools, and readily available expertise in RDBMS systems. However, the querying component of RDBMS technology suffers from performance and optimization problems stemming from the very nature of the relational data model. More specifically, during query processing, the relational data model requires a mechanism that locates the raw data elements that match the query. Moreover, to support queries that involve aggregation operations, such aggregation operations must be performed over the raw data elements that match the query. For large multi-dimensional databases, a naive implementation of these operations involves computational intensive table scans that lead to unacceptable query response times.
In order to better understand how the prior art has approached this problem, it will be helpful to briefly describe the relational database model. According to the relational database model, a relational database is represented by a logical schema and tables that implement the schema. The logical schema is represented by a set of templates that define one or more dimensions (entities) and attributes associated with a given dimension. The attributes associated with a given dimension includes one or more attributes that distinguish it from every other dimension in the database (a dimension identifier). Relationships amongst dimensions are formed by joining attributes. The data structure that represents the set of templates and relations of the logical schema is typically referred to as a catalog or dictionary. Note that the logical schema represents the relational organization of the database, but does not hold any fact data per se. This fact data is stored in tables that implement the logical schema.
Star schemas are frequently used to represent the logical structure of a relational database. The basic premise of star schemas is that information can be classified into two groups: facts and dimensions. Facts are the core data elements being analyzed. For example, units of an individual item sold are facts, while dimensions are attributes about the facts. For example, dimensions are the product types purchased and the data purchase. Business questions against this schema are asked by looking up specific facts (UNITS) through a set of dimensions (MARKETS, PRODUCTS, PERIOD). The central fact table is typically much larger than any of its dimension tables.
An exemplary star schema is illustrated in FIG. 17A for suppliers (the “Supplier” dimension) and parts (the “Parts” dimension) over time periods (the “Time-Period” dimension). It includes a central fact table “Supplied-Parts” that relates to multiple dimensions—the “Supplier”, “Parts” and “Time-Period” dimensions. A central fact table and a dimension table for each dimension in the logical schema of FIG. 17A may be used to implement this logical schema. A given dimension table stores rows (instances) of the dimension defined in the logical schema. Each row within the central fact table includes a multi-part key associated with a set of facts (in this example, a number representing a quantity). The multi-part key of a given row (values stored in the S#,P#,TP# fields as shown) points to rows (instances) stored in the dimension tables described above. A more detailed description of star schemas and the tables used to implement star schemas may be found in C. J. Date, “An Introduction to Database Systems,” Seventh Edition, Addison-Wesley, 2000, pp. 711-715, herein incorporated by reference in its entirety.
When processing a query, the tables that implement the schema are accessed to retrieve the facts that match the query. For example, in a star schema implementation as described above, the facts are retrieved from the central fact table and/or the dimension tables. Locating the facts that match a given query involves one or more of the join operations. Moreover, to support queries that involve aggregation operations, such aggregation operations must be performed over the facts that match the query. For large multi-dimensional databases, a naive implementation of these operations involves computational intensive table scans that typically lead to unacceptable query response times. Moreover, since the fact tables are pre-summarized and aggregated along business dimensions, these tables tend to be very large. This point becomes an important consideration of the performance issues associated with star schemas. A more detailed discussion of the performance issues (and proposed approaches that address such issues) related to joining and aggregation of star schema is now set forth.
The first performance issue arises from computationally intensive table scans that are performed by a naive implementation of data joining. Indexing schemes may be used to bypass these scans when performing joining operations. Such schemes include B-tree indexing, inverted list indexing and aggregate indexing. A more detailed description of such indexing schemes can be found in “The Art of Indexing”, Dynamic Information Systems Corporation, October 1999. All of these indexing schemes replace table scan operations (involved in locating the data elements that match a query) with one or more index lookup operation. Inverted list indexing associates an index with a group of data elements, and stores (at a location identified by the index) a group of pointers to the associated data elements. During query processing, in the event that the query matches the index, the pointers stored in the index are used to retrieve the corresponding data elements pointed therefrom. Aggregation indexing integrates an aggregation index with an inverted list index to provide pointers to raw data elements that require aggregation, thereby providing for dynamic summarization of the raw data elements that match the user-submitted query.
These indexing schemes are intended to improve the join operations by replacing table scan operations with one or more index lookup operation in order to locate the data elements that match a query. However, these indexing schemes suffer from various performance issues as follows:                Since the tables in the star schema design typically contain the entire hierarchy of attributes (e.g. in a PERIOD dimension, this hierarchy could be day>week>month>quarter>year), a multipart key of day, week, month, quarter, year has to be created; thus, multiple meta-data definitions are required (one of each key component) to define a single relationship; this adds to the design complexity, and sluggishness in performance.        Addition or deletion of levels in the hierarchy will require physical modification of the fact table, which is a time consuming process that limits flexibility.        Carrying all the segments of the compound dimensional key in the fact table increases the size of the index, thus impacting both performance and scalability.        
Another performance issue arises from dimension tables that contain multiple hierarchies. In such cases, the dimensional table often includes a level of hierarchy indicator for every record. Every retrieval from the fact table that stores details and aggregates must use the indicator to obtain the correct result, which impacts performance. The best alternative to using the level indicator is the snowflake schema. In this schema, aggregate tables are created separately from the detail tables. In addition to the main fact tables, snowflake schema contains separate fact tables for each level of aggregation. Notably, the snowflake schema is even more complicated than a star schema, and often requires multiple SQL statements to get the results that are required.
Another performance issue arises from the pairwise join problem. Traditional RDBMS engines are not design for the rich set of complex queries that are issued against a star schema. The need to retrieve related information from several tables in a single query—“join processing”—is severely limited. Many RDBMSs can join only two tables at a time. If a complex join involves more than two tables, the RDBMS needs to break the query into a series of pairwise joins. Selecting the order of these joins has a dramatic performance impact. There are optimizers that spend a lot of CPU cycles to find the best order in which to execute those joins. Unfortunately, because the number of combinations to be evaluated grows exponentially with the number of tables being joined, the problem of selecting the best order of pairwise joins rarely can be solved in a reasonable amount of time.
Moreover, because the number of combinations is often too large, optimizers limit the selection on the basis of a criterion of directly related tables. In a star schema, the fact table is the only table directly related to most other tables, meaning that the fact table is a natural candidate for the first pairwise join. Unfortunately, the fact table is the very largest table in the query, so this strategy leads to selecting a pairwise join order that generates a very large intermediate result set, severely affecting query performance.
There is an optimization strategy, typically referred to as Cartesian Joins, that lessens the performance impact of the pairwise join problem by allowing joining of unrelated tables. The join to the fact table, which is the largest one, is deferred until the very end, thus reducing the size of intermediate result sets. In a join of two unrelated tables every combination of the two tables' rows is produced, a Cartesian product. Such a Cartesian product improves query performance. However, this strategy is viable only if the Cartesian product of dimension rows selected is much smaller than the number of rows in the fact table. The multiplicative nature of the Cartesian join makes the optimization helpful only for relatively small databases.
In addition, systems that exploit hardware and software parallelism have been developed which lessens the performance issues set forth above. Parallelism can help reduce the execution time of a single query (speed-up), or handle additional work without degrading execution time (scale-up). For example, Red Brick™ has developed STARjoin™ technology that provides high speed, parallelizable multi-table joins in a single pass, thus allowing more than two tables to be joined in a single operation. The core technology is an innovative approach to indexing that accelerates multiple joins. Unfortunately, parallelism can only reduce, not eliminate, the performance degradation issues related to the star schema.
One of the most fundamental principles of the multidimensional database is the idea of aggregation. The most common aggregation is called a roll-up aggregation. This type is relatively easy to compute: e.g. taking daily sales totals and rolling them up into a monthly sales table. The more difficult are analytical calculations, the aggregation of Boolean and comparative operators. However these are also considered as a subset of aggregation.
In a star schema, the results of aggregation are summary tables. Typically, summary tables are generated by database administrators who attempt to anticipate the data aggregations that the users will request, and then pre-build such tables. In such systems, when processing a user-generated query that involves aggregation operations, the pre-built aggregated data that matches the query is retrieved from the summary tables (if such data exists). FIGS. 18A and 18B illustrate a multi-dimensional relational database using a star schema and summary tables. In this example, the summary tables are generated over the “time” dimension storing aggregated data for “month”, “quarter” and “year” time periods as shown in FIG. 18B. Summary tables are in essence, additional fact tables of higher levels. They are attached to the basic fact table creating a snowflake extension of the star schema. There are hierarchies among summary tables because users at different levels of management require different levels of summarization. Choosing the level of aggregation is accomplished via the “drill-down” feature.
Summary tables containing pre-aggregated results typically provide for improved query response time with respect to on-the-fly aggregation. However, summary tables suffer from some disadvantages:                summary tables require that database administrators anticipate the data aggregation operations that users will require; this is a difficult task in large multi-dimensional databases (for example, in data warehouses and data mining systems), where users always need to query in new ways looking for new information and patterns.        summary tables do not provide a mechanism that allows efficient drill down to view the raw data that makes up the summary table—typically a table scan of one or more large tables is required.        querying is delayed until pre-aggregation is completed.        there is a heavy time overhead because the vast majority of the generated information remains unvisited.        there is a need to synchronize the summary tables before the use.        the degree of viable parallelism is limited because the subsequent levels of summary tables must be performed in pipeline, due to their hierarchies.        for very large databases, this option is not valid because of time and storage space.Note that it is common to utilize both pre-aggregated results and on-the-fly aggregation in support aggregation. In these systems, partial pre-aggregation of the facts results in a small set of summary tables. On-the-fly aggregation is used in case the required aggregated data does not exist in the summary tables.        
Note that in the event that the aggregated data does not exist in the summary tables, the table join operations and the aggregation operations are performed over the raw facts in order to generate such aggregated data. This is typically referred to as on-the-fly aggregation. In such instances, aggregation indexing is used to mitigate the performance of multiple data joins associated with dynamic aggregation of the raw data. Thus, in large multi-dimensional databases, such dynamic aggregation may lead to unacceptable query response times.
In view of the problems associated with joining and aggregation within RDBMS, prior art ROLAP systems have suffered from essentially the same shortcomings and drawbacks of their underlying RDBMS.
While prior art MOLAP systems provide for improved access time to aggregated data within their underlying MDD structures, and have performance advantages when carrying out joining and aggregation operations, prior art MOLAP architectures have suffered from a number of shortcomings and drawbacks. More specifically, atomic (raw) data is moved, in a single transfer, to the MOLAP system for aggregation, analysis and querying. Importantly, the aggregation results are external to the DBMS. Thus, users of the DBMS cannot directly view these results. Such results are accessible only from the MOLAP system. Because the MDD query processing logic in prior art MOLAP systems is separate from that of the DBMS, users must procure rights for access to the MOLAP system and be instructed (and be careful to conform to such instructions) to access the MDD (or the DBMS) under certain conditions. Such requirements can present security issues, highly undesirable for system administration. Satisfying such requirements is a costly and logistically cumbersome process. As a result, the widespread applicability of MOLAP systems has been limited.
Thus, there is a great need in the art for an improved mechanism for joining and aggregating data elements within a database management system (e.g., RDBMS), and for integrating the improved database management system (e.g., RDBMS) into informational database systems (including the data warehouse and OLAP domains), while avoiding the shortcomings and drawbacks of prior art systems and methodologies.